Quantum Computation and Communication with Qubit Systems

Chapter 3 Quantum communication in quantum networks 3.1 Introduction O ne of the problems arising in the design of a feasible quantum computer is how to build up quantum wires, i.e. wires able to transmit quantum information from one end to another. The quantum data bus design involves the choice of the technology to be used in order to achieve an optimal data transfer. In this chapter we will consider channels composedbya sequenceofinteracting electron spins, usuallycalled spin chains in short. A spin chain is a permanently coupled 1D system of electron spins. When a quantum state is placed on one end of it, the state will be dynamically (due to quantum time evolution, see appendix for the details) transmitted to the other end with some efficiency if spins are coupled by an electromagnetic exchange interaction (further de- tails in the appendix). However, such a data-bus requires the ability to modulate the strength or nature of interactions between pairs of adjacent spins in time. For the typi- cal use in quantum computer we should utilize systems that require a very low control, as suitable candidates for connecting quantum registers. This is because in the normal use of “data-buses”, such as to denote a cable connecting two computers, we mostly let the information flow through it in its own natural way, thanks to the metal conduction properties. A spin chain in which inter-spin interactions are permanent, i.e. the inter- action don’t vary with time, is an example of a spin chain, that does not require a large amount of control to be used. In the following we will define the spin chain model, the natural extension to spin network and the conditions for having an high quality transfer on quantum communication devices. 3.1.1 Spin chains and the exchange interaction In quantum mechanics, spins are systems characterized by small quantized magnetic moments. The mutual interactions of these spins makes them prefer alignment or anti- alignment with respect to each other, resulting in diverse phenomena such as ferromag- netism and anti-ferromagnetism. A spin chain models a large class of such materials in which the spins are arranged in a one dimensional lattice and permanently coupled to each other, usually with an interaction strength decreasing with distance. A com- mon form of the Hamiltonian, i.e. the matrix (or in general the mathematical operator)